Due Process and Military Detention Amendments Act of 2013 - Amends the National Defense Authorization Act for Fiscal Year 2012 (such Act) to provide that, in the case of a person detained in the United States pursuant to the Authorization for Use of Military Force or such Act, disposition under the law of war shall occur immediately upon custody and shall only mean transfer for trial and proceedings with all due process rights as provided under the Constitution.

Prohibits any person detained, captured, or arrested in the United States or a U.S. territory or possession from being transferred to the custody of the Armed Forces for detention under the Authorization for Use of Military Force or such Act.

Repeals the requirement of detention in military custody pending disposition under the law of war for an individual determined to be a member or part of al Qaeda or an associated force who has participated in planning or carrying out an attack or attempted attack against the United States or its coalition partners.